Hello Lawrence, Thanks for the suggestion. I recently figured out how to use gmsh and will try and import something into firedrake today and see what that does. But if it is because the PV is discontinuous, good observation, then I suppose I could interpolate into a CG basis and write that to a file? Might be expensive, and even silly, but I presume that should smooth things quite a bit. Francis ------------------ Francis Poulin Associate Professor Department of Applied Mathematics University of Waterloo email: fpoulin@uwaterloo.ca Web: https://uwaterloo.ca/poulin-research-group/ Telephone: +1 519 888 4567 x32637 ________________________________________ From: firedrake-bounces@imperial.ac.uk [firedrake-bounces@imperial.ac.uk] on behalf of Lawrence Mitchell [lawrence.mitchell@imperial.ac.uk] Sent: Thursday, June 16, 2016 9:19 AM To: firedrake@imperial.ac.uk Subject: Re: [firedrake] instability of a vortex in firedrakeQG On 16/06/16 14:02, Francis Poulin wrote:
Hello,
I recently posted a video on youtube that shows the evolution of the perturbation Potential Vorticity for a Gaussian vortex. Initially you see a tripole structure and then a mode 2 structure that is well predicted by the linear theory. This is all done using the QG firedrake code that we've been developing.
One thing that is less than ideal is that I am using white noise for the initial perturbations. Someone mentioned that I should probably solve the Poisson problem where white noise is the RHS, and that should clean things up. I will try and do that but it seems that early on, even after the perturbations establish themselves you can still see the grid. In this case I am using a 400x400 rectangular grid. Do people think that an unstructured mesh might make the grid less apparent?
Maybe part of the problem is with how it's being plotted in VisIt, I'm not sure but I thought I would ask people's advice.
One thing that may be going on is that the PV lives in a discontinuous space. We write this to the visualisation file as a discontinuous field so if there are jumps in the PV then you will see those in the solution. As you say, it may well be the case that because the mesh is so regular, you get a very symmetric pattern of jumps which exhibits itself in this way. But it does look a little odd. As you say, you could try with an unstructured mesh (just make an appropriate resolution one with gmsh) to see if the pattern still exhibits. Cheers, Lawrence